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- Francesco Barioli, Wayne Barrett, +7 authors Hein van der Holst
- 2010

Abstract. The zero forcing number Z(G), which is the minimum number of vertices in a zero forcing set of a 1 graph G, is used to study the maximum nullity/minimum rank of the family of symmetric matrices described by 2 G. It is shown that for a connected graph of order at least two, no vertex is in every zero forcing set. The positive 3 semidefinite zero… (More)

- Wayne Barrett, Sean M. Garber
- Surgical endoscopy
- 2003

Surgical smoke is omnipresent in the day-to-day life of the surgeon and other medical personnel who work in the operating room. In addition, patients are also exposed, especially and uniquely so in laparoscopic cases where smoke is created and trapped in a closed and absorptive space. Surgical smoke has typically been produced by electrocautery but is now… (More)

- D . G . Michael, Penelope Adamson, +271 authors R . Zwaska
- Physical review letters
- 2006

This Letter reports results from the MINOS experiment based on its initial exposure to neutrinos from the Fermilab NuMI beam. The rates and energy spectra of charged current nu(mu) interactions are compared in two detectors located along the beam axis at distances of 1 and 735 km. With 1.27 x 10(20) 120 GeV protons incident on the NuMI target, 215 events… (More)

- Wayne Barrett, CHARLES R. JOHNSONy
- 1993

We consider the question of whether a real partial positive de nite matrix (in which the speci ed o -diagonal entries consist of a full n cycle) has a positive de nite completion. This lies in contrast to the previously studied chordal case. We give two solutions. In one, we describe about n 2 independent conditions on angles associated with a normalization… (More)

- Penelope Adamson, C . Andreopoulos, +168 authors R . Zwaska
- Physical review letters
- 2008

This Letter reports new results from the MINOS experiment based on a two-year exposure to muon neutrinos from the Fermilab NuMI beam. Our data are consistent with quantum-mechanical oscillations of neutrino flavor with mass splitting |Deltam2| = (2.43+/-0.13) x 10(-3) eV2 (68% C.L.) and mixing angle sin2(2theta) > 0.90 (90% C.L.). Our data disfavor two… (More)

Let G be an undirected graph on n vertices and let S(G) be the set of all real symmetric n × n matrices whose nonzero off-diagonal entries occur in exactly the positions corresponding to the edges of G. The inverse inertia problem for G asks which inertias can be attained by a matrix in S(G). We give a complete answer to this question for trees in terms of… (More)

- Wayne Barrett, Steve Butler, +5 authors Michael K Young
- 2014

Given an n × n matrix, its principal rank characteristic sequence is a sequence of length n + 1 of 0s and 1s where, for k = 0, 1, . . . , n, a 1 in the kth position indicates the existence of a principal submatrix of rank k and a 0 indicates the absence of such a submatrix. The principal rank characteristic sequences for symmetric matrices over various… (More)

- Francesco Barioli, Wayne Barrett, +5 authors Hein van der Holst
- Journal of Graph Theory
- 2013

Tree-width, and variants that restrict the allowable tree decompositions, play an important role in the study of graph algorithms and have application to computer science. The zero forcing number is used to study the maximum nullity/minimum rank of the family of symmetric matrices described by a graph. We establish relationships between these parameters,… (More)

Let F be a field, G = (V, E) be an undirected graph on n vertices, and let S(F,G) be the set of all symmetric n × n matrices whose nonzero off-diagonal entries occur in exactly the positions corresponding to the edges of G. For example, if G is a path, S(F,G) consists of the symmetric irreducible tridiagonal matrices. Let mr(F,G) be the minimum rank over… (More)

- Wayne Barrett, Jason Grout
- 2008

Abstract Our main result is a sharp bound for the number of vertices in a minimal forbidden subgraph for the graphs having minimum rank at most 3 over the finite field of order 2. We also list all 62 such minimal forbidden subgraphs. We conclude by exploring how some of these results over the finite field of order 2 extend to arbitrary fields and… (More)